In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as HellmanFeynman forces, require, because of practical computational reasons, the discretized charge density and wave functions having continuous second derivatives in the whole solution domain. We describe an application of isogeometric analysis (IGA), a spline modification of finite element method (FEM), to achieve the required continuity. The novelty of our approach is in employing the technique of Bézier extraction to add the IGA capabilities to our FEM based code for ab-initio calculations of electronic states of non-periodic systems within the density-functional framework, built upon the open source finite element package SfePy. We compare FEM and IGA in benchmark problems and several numerical results are presented.
Behavior of various, even hypothetical, materials can be predicted via ab-initio electronic structure calculations providing all the necessary information: the total energy of the system and its derivatives. In case of non-periodic structures, the existing well-established methods for electronic structure calculations either use special bases, predetermining and limiting the shapes of wave functions, or require artificial computationally expensive arrangements, like large supercells. We developed a new method for non-periodic electronic structures based on the density functional theory, environment-reflecting pseudopotentials and the isogeometric analysis with Bézier extraction, ensuring continuity for all quantities up to the second derivative. The approach is especially suitable for calculating the total energy derivatives and for molecular-dynamics simulations. Its main assets are the universal basis with the excellent convergence control and the capability to calculate precisely the non-periodic structures even lacking in charge neutrality. Within the present paper, convergence study for isogeometric analysis vs. standard finite-element approach is carried out and illustrated on sub-problems that appear in our electronic structure calculations method: the Poisson problem, the generalized eigenvalue problem and the density functional theory Kohn-Sham equations applied to a benchmark problem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.